Existing localization systems typically use particle filters and a priori maps. For example, in a typical prior art system, a set of particles (or hypotheses) is used to represent the estimated position of a mobile device, such as a mobile robot. As the robot moves, the particles (or hypotheses of sensor node positions) are updated using a statistical motion model to arrive at a new estimate of the robot's position. Generally, without the introduction of any additional knowledge, the more a robot moves, the more dispersed the particles will become. With the introduction of known obstacles or observable structures, however, robot motion can reduce the particle dispersion because these obstacles or structures constrain allowable particle movement, and those particles that violate these constraints can be eliminated. In general, however, once these types of constraints have been applied, there is no further benefit to applying them again until particles are once again moved.